Since it is unlikely that the Planck observation and/or the local distance ladder measurements suffer from considerable unaccounted systematic errors [1]}, [2]}, [3]}, [4]}, [5]}, increasing attention is focusing on the possibility that \(H_0\)  tension might be the first sign for physics beyond \(\Lambda \) CDM. The most economical modifications to the concordance model include replacing the cosmological constant \(\Lambda \)  by a dark energy component with equation of state \(w<-1\)  [6]}, [7]} (i.e. phantom dark energy) and introducing some form of dark radiation [8]}, [9]}, [10]}, [11]}, [12]}, [13]} (so as to raise the extra relativistic degrees of freedom \(N_{eff}\)  beyond 3.046). Although these two modifications can help with the \(H_0\)  tension, it is worth to mention that phantom dark energy and extra relativistic species are disfavored from both baryonic acoustic oscillations (BAO) and Type Ia supernovae (SN Ia) data and from a model comparison point of view [14]}. In recent years, lots of other scenarios attempting to solve the \(H_0\)  tension have been examined, including (but ont limited to) an exotic early dark energy that acts as a cosmological constant before a critical redshift \(z_c\)  but whose density then dilutes faster than radiation [15]}, [16]}, [17]}, [18]}, interactions between dark matter and dark energy [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, a vacuum phase transition [26]}, [27]}, modifications to gravity [28]}, [29]}, [30]}.
